MCQ
If $\triangle\text{ABC}\sim\triangle\text{DEF}$ such that DE = 3cm, EF = 2cm, DF = 2.5cm, BC = 4cm, then perimeter of $\triangle\text{ABC}$ is:
- A18cm.
- B20cm.
- C12cm.
- ✓15cm.
✓
Answer
Correct option: D.
15cm.
$\triangle\text{ABC}\sim\triangle\text{DEF}$
DE = 3cm, EF = 2cm, DF = 2.5cm, BC = 4cm
$\because\triangle\text{ABC}\sim\triangle\text{DEF}$
$\therefore$ Perimeter of $\triangle\text{DEF}$
= DE + EF + DF
= 3 + 2 + 2.5 = 7.5cm
Now $\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{AC}}{\text{DF}}=\frac{\text{AB}+\text{BC}+\text{CA}}{\text{DE}+\text{EF}+\text{DF}}$
$=\frac{4}{2}=\frac{\text{AB}+\text{BC}+\text{CA}}{7.5}$
$\Rightarrow\text{AB}+\text{BC}+\text{CA}=\frac{4\times7.5}{2}=15$
$\therefore$ Perimeter of $\triangle\text{ABC}=15\text{cm}.$
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